CHAPTER 3 CHARACTERISTICS OF SUDDEN HIGH
3.3 Mechanism of sudden high waves
of each figure is the physical pattern during the 15 day period. Blue line is for Gangneung and green line is for Wangdolcho. The second panel is the PC time series and the third panel is the reconstructed significant wave height of the mode.
The last panel is the zoom view of the reconstructed significant wave height, which is to check if peak occurs or not during the reported marine accidents date on 21-23 October 2005. The shapes of the second and third CSLVs are similar to sudden high waves, so they were regarded as the physical process of sudden high waves.
Also, the second and third modes have a large peak on 21-23 October 2005.
Therefore, two modes were considered as the physical process of sudden high waves.
0 5 10 15 20 25 30 35 40
0 0.05 0.1 0.15 0.2 0.25
Number of Mode
Normalized Eigenvalue
0 5 10 15 20 25 30 35 40
0.2 0.4 0.6 0.8 1
Number of Mode
Cumulative Eigenvalue
Fig. 3.7 Eigenvalues of CSEOF modes for significant wave height data from KIOST
1 5 10 15 -5
0 5
H CSLV
Gangneung Wangdolcho
2005-10-01-1 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-27 0
1
H PCT
2005-10-01-2 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-27 0
2
Reconstructed H
2005-10-01 2005-10-06 2005-10-11 2005-10-16 2005-10-21 2005-10-26-1 2005-10-31 0
1
Zoom view of Reconstructed H
Fig. 3.8 CSEOF mode 1 of significant wave height data from KIOST
1 5 10 15 -5
0 5
H CSLV
Gangneung Wangdolcho
2005-10-01-1 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-27 0
1
H PCT
2005-10-01-5 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-27 0
5
Reconstructed H
2005-10-01 2005-10-06 2005-10-11 2005-10-16 2005-10-21 2005-10-26-5 2005-10-31 0
5
Zoom view of Reconstructed H
Fig. 3.9 CSEOF mode 2 of significant wave height data from KIOST
1 5 10 15 -5
0 5
H CSLV
Gangneung Wangdolcho
2005-10-01-1 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-27 0
1
H PCT
2005-10-01-2 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-27 0
2
Reconstructed H
2005-10-01 2005-10-06 2005-10-11 2005-10-16 2005-10-21 2005-10-26-2 2005-10-31 0
2
Zoom view of Reconstructed H
Fig. 3.10 CSEOF mode 3 of significant wave height data from KIOST
To detect sudden high wave modes, the index of sudden high waves, 𝐻2𝐿 was analyzed using CSEOF analysis. It is decomposed into 33 modes. Fig. 3.11 presents the normalized and cumulative eigenvalues of CSEOF modes for the index. Fig. 3.12-Fig.3.14 show the first 3 modes for the index. The shapes of the modes are similar to those of significant wave height but they are more distinct.
The first 3 modes are similar to sudden high waves. However, comparing the reported events and the reconstructed series, the third mode did not correspond.
Therefore, the first two modes were considered as the physical process of sudden high waves.
5 10 15 20 25 30
0 0.1 0.2 0.3 0.4
Number of Mode
Normalized Eigenvalue
5 10 15 20 25 30
0.2 0.4 0.6 0.8 1
Number of Mode
Cumulative Eigenvalue
Fig. 3.11 Eigenvalues of CSEOF modes for sudden high wave index
1 5 10 15 -5
0 5
H2L CSLV
Gangneung Wangdolcho
2005-10-01 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-27 -1000
0 1000
H2L PCT
2005-10-01 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-27 -5000
0 5000
Reconstructed H2L
2005-10-01 2005-10-06 2005-10-11 2005-10-16 2005-10-21 2005-10-26 2005-10-31 -2000
0 2000
Zoom view of Reconstructed H2L
Fig. 3.12 CSEOF mode 1 of sudden high wave index
1 5 10 15 -5
0 5
H2L CSLV
Gangneung Wangdolcho
2005-10-01 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-27 -1000
0 1000
H2L PCT
2005-10-01 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-27 -5000
0 5000
Reconstructed H2L
2005-10-01 2005-10-06 2005-10-11 2005-10-16 2005-10-21 2005-10-26 2005-10-31 -5000
0 5000
Zoom view of Reconstructed H2L
Fig. 3.13 CSEOF mode 2 of sudden high wave index
1 5 10 15 -10
0 10
H2L CSLV
Gangneung Wangdolcho
2005-10-01 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-27 -1000
0 1000
H2L PCT
2005-10-01 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-27 -5000
0 5000
Reconstructed H2L
2005-10-01 2005-10-06 2005-10-11 2005-10-16 2005-10-21 2005-10-26 2005-10-31-500 0
500
Zoom view of Reconstructed H2L
Fig. 3.14 CSEOF mode 3 of sudden high wave index
Next, regression analysis was conducted to find the consistent physical relation between waves and meteorological variables. Fig. 3.15 and Fig. 3.16 show comparisons of the first two modes of the regressed sea level pressure PC time series and wind speed PC time series with the significant wave height PC time series, respectively.
By multiplying the regression coefficients to CSLVs of meteorological variables, the processes of meteorological variables corresponding to the physical processes of significant wave height were produced. Fig. 3.17 shows the evolution of spatial patterns of the second mode of significant wave height and meteorological variables. They are the snapshots of the spatial patterns at the point of the red spot on the graph of the significant wave height CSLV. It shows the physical patterns of the meteorological variables when the second mode of physical pattern of the wave height occurred. Until two days before the rapid growth of the wave height, sea level pressure patterns show high pressure in the west of Korea and low pressure in the east and wind had blown continuously. From two days before the occurrence of sudden high waves, high pressure stayed over the east coast of Korea and wind on the east coast of Korea was very weak, but wind in the northwest of Japan was strong. The weather in the Korean peninsula was mild in those days. As high pressure moved to the east, the weather condition changed rapidly, so wind speed in the East Sea increased. Low pressure passed to the east side before the wave height grew. There are two peaks in the second mode of CSLV for H. The first peak seemed to be generated by low pressure and easterly wind blowing for 1 day, whereas the second peak seemed to be caused by strong wind. Fig. 3.18 represents the evolution of spatial patterns of the third mode.
Variation of sea level pressure was very small over the period. Wind blew strongly
2005-10-01-3 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-28 -2.5
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Comparison of Hs and Regressed SLP PCTs
Mode: 1, R2: 0.93105
Hs
Regressed SLP
Fig. 3.15 Comparison of the first 2 modes of the regressed sea level pressure PC time series and significant wave height PC time series
2005-10-01-3 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-28
-2 -1 0 1 2 3 4
Comparison of Hs and Regressed SLP PCTs
Mode: 2, R2: 0.82718
Hs
Regressed SLP
2005-10-01-3 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-28 -2.5
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Comparison of Hs and Regressed U10 PCTs
Mode: 1, R2: 0.93661
Hs
Regressed U10
Fig. 3.16 Comparison of the first 2 modes of the regressed wind speed PC time series and significant wave height PC time series
2005-10-01-3 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-28
-2 -1 0 1 2 3 4
Comparison of Hs and Regressed U10 PCTs
Mode: 2, R2: 0.92148
Hs
Regressed U10
over the period, but there was a spatial variation before the rapid increase of the wave height. Wind on the east coast of Korea was very weak, but wind far from the coast was strong. The first peak of the third mode of wave height seemed to be come from the northern part of the East Sea. After the arrival of the first peak of the wave height, wind blew strongly over the East Sea. The second peak seemed to be affected by strong wind near Gangneung.
Fig. 3.19 and Fig. 3.20 show comparisons of the first two modes of the regressed sea level pressure PC time series and wind speed PC time series with the index of sudden high waves, 𝐻2𝐿, respectively. The physical processes of sudden high waves and the corresponding processes of meteorological variables were compared by multiplying the regression coefficients to the CSLVs of meteorological variables. Fig. 3.21 shows the evolution of the spatial patterns of the first mode of sudden high wave index and meteorological variables. The first mode of sudden high wave index has negative values, so sudden high waves will occur when it combines with the negative PC time series. Until the rapid growth of the index, there was spatial variation in wind speed. Wind near the east coast of Korea was very weak, but wind in the northeast part of the East Sea was strong. As the spatial variation reduces gradually, the wind speed increased near the east coast of Korea and the value of index grew rapidly. After the increase of the magnitude of the index, the wind speed decreased gradually on the east coast, but wind in the offshore area blew continuously. It was inferred that the first peak of the index seemed to be affected by the wind speed on the east coast to increase and the second peak seemed to be influenced by wind in the offshore area. For the second mode of sudden high wave index, there was no distinct change in the spatial
1 3 5 7 9 11 13 15 -2
-1 0 1 2
3 CSLV Mode: 2, Time Step: 131
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-2 -1 0 1 2
3 CSLV Mode: 2, Time Step: 171
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-2 -1 0 1 2
3 CSLV Mode: 2, Time Step: 221
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-2 -1 0 1 2
3 CSLV Mode: 2, Time Step: 271
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-2 -1 0 1 2
3 CSLV Mode: 2, Time Step: 281
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-2 -1 0 1 2
3 CSLV Mode: 2, Time Step: 321
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-2 -1 0 1 2
3 CSLV Mode: 2, Time Step: 351
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-2 -1 0 1 2
3 CSLV Mode: 2, Time Step: 371
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
Fig. 3.17 Evolution of spatial patterns for the 2nd mode of significant wave height and meteorological variables
1 3 5 7 9 11 13 15 -1.5
-1 -0.5 0 0.5 1 1.5 2
CSLV Mode: 3, Time Step: 131
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-1.5 -1 -0.5 0 0.5 1 1.5 2
CSLV Mode: 3, Time Step: 171
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-1.5 -1 -0.5 0 0.5 1 1.5 2
CSLV Mode: 3, Time Step: 221
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-1.5 -1 -0.5 0 0.5 1 1.5 2
CSLV Mode: 3, Time Step: 271
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-1.5 -1 -0.5 0 0.5 1 1.5 2
CSLV Mode: 3, Time Step: 281
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-1.5 -1 -0.5 0 0.5 1 1.5 2
CSLV Mode: 3, Time Step: 321
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-1.5 -1 -0.5 0 0.5 1 1.5 2
CSLV Mode: 3, Time Step: 351
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
1 3 5 7 9 11 13 15
-1.5 -1 -0.5 0 0.5 1 1.5 2
CSLV Mode: 3, Time Step: 371
CSLV of Significant Wave Height in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meterological Data
-5 0 5
Fig. 3.18 Evolution of spatial patterns for the 3rd mode of significant wave height and meteorological variables
2005-10-01-5 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-28 -4
-3 -2 -1 0 1 2
Comparison of H2L and Regressed SLP PCTs
Mode: 1, R2: 0.88014
H2L
Regressed SLP
Fig. 3.19 Comparison of the first 2 modes of the regressed sea level pressure PC time series and sudden high wave index PC time series
2005-10-01-5 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-28 -4
-3 -2 -1 0 1 2 3 4 5
Comparison of H2L and Regressed SLP PCTs
Mode: 2, R2: 0.85839
H2L
Regressed SLP
Fig. 3.20 Comparison of the first 2 modes of the regressed wind speed PC time series and sudden high wave index PC time series
2005-10-01-5 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-28 -4
-3 -2 -1 0 1 2
Comparison of H2L and Regressed U 10 PCTs
Mode: 1, R2: 0.98963
H2L
Regressed U10
2005-10-01-5 2008-10-01 2010-10-01 2011-10-01 2012-10-01 2013-02-28 -4
-3 -2 -1 0 1 2 3 4 5
Comparison of H2L and Regressed U
10 PCTs
Mode: 2, R2: 0.98019
H2L
Regressed U10
1 3 5 7 9 11 13 15 -4
-2 0 2 4 6
CSLV Mode: 2, Time Step: 175
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-4 -2 0 2 4 6
CSLV Mode: 2, Time Step: 229
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-4 -2 0 2 4 6
CSLV Mode: 2, Time Step: 283
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-4 -2 0 2 4 6
CSLV Mode: 2, Time Step: 313
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-4 -2 0 2 4 6
CSLV Mode: 2, Time Step: 337
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-4 -2 0 2 4 6
CSLV Mode: 2, Time Step: 349
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-4 -2 0 2 4 6
CSLV Mode: 2, Time Step: 373
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-4 -2 0 2 4 6
CSLV Mode: 2, Time Step: 415
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
Fig. 3.21 Evolution of spatial patterns for the 1st mode of sudden high wave index and meteorological variables
1 3 5 7 9 11 13 15 -5
-4 -3 -2 -1 0 1
CSLV Mode: 1, Time Step: 175
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-5 -4 -3 -2 -1 0 1
CSLV Mode: 1, Time Step: 229
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-5 -4 -3 -2 -1 0 1
CSLV Mode: 1, Time Step: 283
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-5 -4 -3 -2 -1 0 1
CSLV Mode: 1, Time Step: 313
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-5 -4 -3 -2 -1 0 1
CSLV Mode: 1, Time Step: 337
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-5 -4 -3 -2 -1 0 1
CSLV Mode: 1, Time Step: 349
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-5 -4 -3 -2 -1 0 1
CSLV Mode: 1, Time Step: 373
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
1 3 5 7 9 11 13 15
-5 -4 -3 -2 -1 0 1
CSLV Mode: 1, Time Step: 415
CSLV of H2L in Gangneung
128 130 132 134 136 138 140 142
34 36 38 40 42 44
CSLV of Meteorological Data
-1 -0.5 0 0.5 1
Fig. 3.22 Evolution of spatial patterns for the 2nd mode of sudden high wave